Your statements on champion design contradict each other. Originally you said these things had seen no real change in five years, yet just now you talked about overloaded kits and mobility creep, longing for the old way of things. You can't fault something for not changing then complain when it has clearly changed.
Champion select is functional, letting you search alphabetically or by typing in a search bar. Teambuilder could use improvements, but I don't believe it's Teambuilder's UI that's holding it back. People arguing over roles is not a UI problem, but what you proposed is supposedly being worked on.
The only change I personally would want to the Runes and Mastery UI is the ability to rearrange pages, but that's not a problem. T1&T2 Runes are/were (haven't double checked when that was suppose to go live) changed to be significantly cheaper, letting new players try out combinations faster and without as much investment. While these changes might not be what you're looking for, they do help.
As for Lee Sin, in the EU he's been picked a grand total of 6 times out of 25 games. This means that you're more likely to see a game with a Graves, Gnar, Jarvan, Leona, Annie, Ahri, Corki, Lulu, Sivir, Kassadin, LeBlanc, Lissandra, Thresh, or Rek'Sai than you are to see a Lee Sin. Stats from here.
Snowballing... that's a hard one. I've seen some games drag on too long because both teams were too passive and neither one wanted to or was able to snowball. On the flip side, one sided matches aren't fun to watch after the initial shock of how unbalanced the teams are. I know Riot mentioned that they didn't like the "rubber banding" effect that happened in Season 4 where one team would take an inhib, the other team would defend, then they'd take an inhib and the other team defend, which is why they tried to make Season 5 a little bit more snowbally. I can see this one being a matter of preference, and hard to dial into an ideal situation.